Theorems · Theorem · number theory
Polynomial.cyclotomic_prime
∀ (R : Type u_1) [inst : Ring R] (p : ℕ) [hp : Fact (Nat.Prime p)], Polynomial.cyclotomic p R = ∑ i ∈ Finset.range p, Polynomial.X ^ i
If p is prime, then cyclotomic p R = ∑ i ∈ range p, X ^ i.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- Factstatement and proof · cited by 2,726
- Finset.prodproof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- Nat.Primestatement and proof · cited by 2,059
- Polynomial.Xstatement and proof · cited by 1,639
- Finset.rangestatement and proof · cited by 1,341
- Polynomial.mapproof · cited by 806
- Iff.notproof · cited by 489
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_twoproof · cited by 4
- Polynomial.cyclotomic_prime_pow_eq_geom_sumproof · cited by 3
- Polynomial.eval_one_cyclotomic_primeproof · cited by 2
- Polynomial.cyclotomic_threeproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- Polynomial.cyclotomic_prime_mul_X_sub_oneproof · cited by 0